The London-Paris Number Theory Seminar

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The London-Paris Number Theory Seminar meets twice per year, once in London and once in Paris. It is supported by grants from ANR Projet ArShiFo ANR-BLAN-0114, EPSRC Platform Grant EP/I019111/1, PerCoLaTor (Grant ANR-14-CE25), the Heilbronn Institute for Mathematical Research, and ERC Advanced Grant AAMOT.

London organizers: David Burns, Kevin Buzzard Fred Diamond, Yiannis Petridis, Alexei Skorobogatov, Andrei Yafaev, Sarah Zerbes.

Paris organizers: Matthew Morrow, Olivier Fouquet, Michael Harris, Marc Hindry, Benjamin Schraen, Jacques Tilouine.

23rd meeting, Paris.

The 23rd meeting of the LPNTS will take place in Paris (in Jussieu), on 27th and 28th November 2017. The topic is Periods. The room will be Jussieu 1525-502, and here's the schedule:

Monday 27/11/2017:

11.15--12.15 Minhyong Kim -- Gauge theory in arithmetic geometry
12.15--2.15 lunch
2.15--3.15 Jean-Benoît Bost -- Transcendence proofs and infinite-dimensional geometry of numbers
3.15--4.15 Javier Fresán -- Gamma values as exponential periods
4.15--5.00 Tea break
5.00--6.00 Francis Brown

Tuesday 28/11/2017:

9.15--10.15 Tony Scholl
10.15--11.00 Tea break
11.00--12.00 Jie Lin -- On factorization of automorphic periods
12.15 Lunch


Jean-Benoît Bost : Transcendence proofs and infinite-dimensional geometry of numbers.
Abstract : I will explain how some classical transcendence results concerning periods, notably the theorem of Schneider-Lang, may be given "natural proofs" based on the consideration of some infinite dimensional avatars of Euclidean lattices.

Javier Fresán : Gamma values as exponential periods
Abstract: As one can already guess from the Gaussian integral, the values of the gamma function at rational arguments are not expected to be periods, although suitable products of them do become periods of abelian varieties with complex multiplication. To deal with single gamma values, one needs to consider exponential periods instead. I will discuss how a joint work with Peter Jossen, in which we construct a Tannakian category of exponential motives over a subfield of the complex numbers, allows one to explain the transcendence conjectures for gamma values in a natural way.

Jie Lin : On factorization of automorphic periods Abstract: The question on the factorization of automorphic periods was initiated by Shimura where periods refer to the Petersson inner products of algebraic forms. Essentially, he predicted that periods related to Hilbert modular forms, or more generally to algebraic forms on a division algebra, factorize as products of periods indexed by the split archimedean places of the division algebra. The initial conjecture was first proved by M. Harris and completed by H. Yoshida. However, their methods seem very difficult to generalize to higher ranks. In this talk, we will explain a new and simple proof for general rank. We will also explain how to read this factorization from the point of view of motives, and why it is important in the study of special values of L-functions.

Previous meetings:

17th meeting (Jussieu, 10/11/14)
18th meeting (Imperial, 4--5/6/15)
19th meeting (Paris 13, 9/11/15)
20th meeting (UCL, 6--7/6/16)
21st meeting (Jussieu, 14--15/11/16)
22nd meeting (UCL, 5--6/6/17)

This page is maintained by Kevin Buzzard.